A heat shield provides thermal protection to flanges of a high pressure compressor of a gas turbine engine. The flanges are tightly sealed within the heat shield to prevent thermal transfer to the flanges and an inner case wall. Heat shields provide transient passive thermal control of the inner case and flanges. Complete sealing can cause high temperature gradients that could reduce the life of the components contained inside the heat shield and result in slow deflections of the components during thermal transients.